type 7 finding sum difference product based ratio & proportion problems Practice Questions Answers Test with Solutions & More Shortcuts

Question : 21 [SSC CGL Prelim 2002]

The ratio of the number of boys and girls of a school with 504 students is 13 : 11. What will be the new ratio if 12 more girls are admitted?

a) 9 : 10

b) 10 : 9

c) 81 : 91

d) 91 : 81

Answer: (d)

Total numbers of girls in the school

= $504 ×11/{13 + 11}$

= $504 × 11/24$ = 231

Total numbers of boys in the school

= $504 × 13/{13 + 11}$

= $504 × 13/29 = 273$

Now, total no. of girls when 12 more girls are admitted

= 231 + 12 = 243

Required ratio

= 273 : 243 = 91 : 81

Question : 22 [SSC CHSL 2012]

If there is a reduction in the number of workers in a factory in the ratio 15 : 11 and an increment in their wage in the ratio 22 : 25, then the ratio by which the total wage of the workers should be decreased is

a) 3 : 7

b) 3 :5

c) 5 : 6

d) 6 : 5

Answer: (d)

Tricky Approach

Required ratio

= 15 × 22 : 11 × 25 = 6 : 5

Question : 23 [SSC CGL Prelim 1999]

A and B have money in the ratio Rs.2 : 1. If A gives 2 to B, the money will be in the ratio 1 : 1. What were the initial amounts they had?

a) Rs.8 and Rs.4

b) Rs.6 and Rs.3

c) Rs.16 and Rs.8

d) Rs.12 and Rs.6

Answer: (a)

Let A and B have Rs.2x and Rs.x initially.

2x - 2 = x + 2

x = 4

Initial amount with A = Rs.8

Initial amount with B = Rs.4.

Question : 24 [SSC CGL Tier-I 2014]

Two numbers are in the ratio of 3 : 5. If 9 is subtracted from each then they are in the ratio 12 : 23. The smaller number is

a) 28

b) 36

c) 33

d) 55

Answer: (c)

Numbers = 3x and 5x (let)

According to question,

${3x - 9}/{5x - 9} = 12/23$

69x - 207 = 60x - 108

69x - 60x = 207 - 108

9x = 99 ⇒ $x = 99/9$ = 11

Smaller number = 3x = 3 × 11 = 33

Question : 25 [SSC Delhi Police 2012]

Two numbers are in the ratio of 3 : 5. If 9 be subtracted from each, then they are in the ratio of 12 : 23. Find the numbers.

a) 33, 55

b) 60, 69

c) 36, 115

d) 15, 28

Answer: (a)

According to the question,

${3x - 9}/{5x - 9} = 12/23$

(Numbers = 3x and 5x )

69x - 207 = 60x - 108

9x = 207 - 108 = 99

x = 11

Required numbers

3 × 11 = 33 and 5 × 11 = 55

Using Rule 35,

Here, a = 3, b = 5, c = 12,

d = 23, x = 9

1st Number = ${xa(d-c)}/{ad-bc}$

= ${9 × 3(23 - 12)}/{3 × 23 - 5 × 12}$

= ${27 × 11}/{69 - 60}$

= ${27 × 11}/9$= 33

2nd Number= ${xb(d-c)}/{ad-bc}$

= ${9 × 5(23 - 12)}/{3 × 23 - 5 × 12}$

= ${45 × 11}/{69 - 60}$

= ${45 × 11}/9$ = 55

Numbers are 33, 55

IMPORTANT quantitative aptitude EXERCISES

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